Photograph taken during the 64th ERSA Congress in Athens, 2025.
The questions were submitted to J. Paul Elhorst in writing, and his responses were received on 11 September 2026.
J. Paul Elhorst is Emeritus Professor of Spatial Econometrics at the University of Groningen and holds a PhD in Economics and an MSc in Econometrics from the University of Amsterdam. His career began at the Agricultural Economics Research Institute in The Hague, where working with farm-level panel data laid the foundations for his later research on spatial panel models.
His work has helped extend spatial econometrics beyond its early cross-sectional foundations. His book, Spatial Econometrics: From Cross-sectional Data to Spatial Panels, brings together this development, while his research addresses questions that applied researchers encounter when choosing a model, representing spatial relationships, and interpreting direct and indirect effects.
A recurring theme in Elhorst’s work is the need to “raise the bar” in applied spatial econometric research. The phrase connects his concern with research quality to questions of model specification, theoretical justification, and empirical practice. Alongside his methodological contributions, he served as Editor-in-Chief of Spatial Economic Analysis from 2015 to 2023.
In the conversation that follows, Elhorst traces his path from panel-data econometrics to spatial econometrics and reflects on the changes he describes as four generations of spatial econometric models. He discusses the choice between competing specifications, the value of sharing computer code, and the challenge of estimating spatial relationships when the true spatial weights matrix is unknown. His account of the field’s future brings these questions together in dynamic spatial models with common factors, while returning to the importance of learning from empirical applications.
Academic profile of J. Paul Elhorst
From Applied Regional Research to Spatial Econometrics
HSSL: You began your career as an economist at the Agricultural Economics Research Institute, working on concrete regional problems, long before you became known for spatial econometrics. How did you get from there to here-and did beginning on the applied side shape the way you think about space?
J. Paul Elhorst: I studied econometrics at the University of Amsterdam, with Spatial Economics and Transport Economics as electives. Through my work at the Agricultural Economics Research Institute, I became familiar with panel data econometrics. This institute collected and managed a panel of approximately 1,000 farms spread across the Netherlands. I wrote my PhD thesis at this institute using this data set, which resulted in my first two international papers, both published in the European Journal of Agricultural Economics. After I finished my PhD, I moved to the University of Groningen to become part of the research group in Spatial Economics.
There I started to work with regional EU data made available by Eurostat on labor force participation, unemployment, GDP per capita and employment growth. To analyze these data, I used econometric models for panel data and estimation techniques I learned at the Agricultural Economics Research Institute. Initially, these models and techniques were non-spatial. Due to visiting international conferences and my background in econometrics, I became interested in spatial econometrics. It struck me that all the presentations I attended in this field focused on cross-sectional data only rather than on panel data. Due to my background on panel data, I started to ask myself why. Consequently, I embarked on this path. This resulted in my first paper on this topic in Geographical Analysis in 2001: Dynamics in space and time.
Raising Standards in Applied Spatial Econometric Research
HSSL: “Raising the bar” was not only the title of your 2010 paper; from 2016 to 2023, it became the organising idea of a recurring editorial series in Spatial Economic Analysis. What were you hoping to achieve with it? And over those eight years, what did you see change-both in the questions researchers asked and in the way they went about answering them?
J. Paul Elhorst: My drive was and still is to further and further improve the quality of research and, in my case, the quality of research based on spatial econometric models. I summarized the changes I have seen as four generations of spatial econometric models. The first generation consists of models based on cross-sectional data. The second generation comprises non-dynamic models based on spatial panel data. These models might just pool time-series cross-sectional data, but more often they control for fixed or random spatial and/or time-period specific effects. The third generation encompasses dynamic spatial panel data models, while the fourth generation also controls for common factors, either in the form of cross-sectional averages or principal components.
Choosing a Spatial Model: From SLX to the General Nesting Model
HSSL: Applied researchers face a long menu of specifications-SAR, SEM, SDM, SLX, and the general nesting model. With Solmaria Halleck Vega, you argued that when theory offers no clear guidance, the SLX model provides a useful point of departure. More than a decade later, is that still the advice you would give?
J. Paul Elhorst: In empirical research the SLX model might be a better starting point than the SAR, SEM and SARAR models which dominate the spatial econometric-theoretical literature, because the number of spatial lags in the regressors (K in total) often exceeds the number of spatial lags in the dependent variable and the error term (2 in total): K > 2. The next step is to investigate whether a spatial lag in the dependent variable or in the error term also need to be included. The inclusion of a spatial lag in the dependent variable must be substantiated by economic theory, an issue that is often wrongly disregarded. Whether or not to include a spatial lag in the error term is more an empirical question, but note its inclusion should not change the parameter estimates significant statistically, another issue that is often wrongly disregarded. If so, it points to misspecification problems. The ideal is to include both lags, leading to the GNS model, and to test which spatial lags are not significant. I am working on this model at the moment based on new insights.
Open Code, Reproducibility, and a New Generation of Researchers
HSSL: For years, you have made the MATLAB routines accompanying your book freely available through spatial-panels.com, allowing researchers to reproduce its results and apply the models to their own data. Did you expect that code to have such a lasting teaching role? And what would you tell students starting out today in R or Python?
J. Paul Elhorst: If, as a researcher, you invest time and effort in collecting data, finding the best-fitting model, and developing computer code to estimate the parameters of this model, you would prefer to keep that to yourself and not disclose it. However, a publication gains much more impact, in term of citations, recognition and image, if you do share it. I learned this from other researchers who were active in this field at the time. It is the best advice I have ever received. When I started sharing my computer code, Matlab was the norm. Today, it is R and Python. As always, you have to keep up with new developments.
Rethinking Spatial Weights: Estimation and Uncertainty
HSSL: The spatial weights matrix has always been one of the most contested choices in the field. In your recent work, you allow distance decay to be estimated rather than imposed and show that indirect effects are particularly sensitive to how spatial distance is defined. How far can this be taken-and is there a risk of fitting the very spatial structure we set out to explain?
J. Paul Elhorst: Parameterizing the spatial weight matrix by one or even better multiple parameters and adopting a different spatial weight matrix for every spatial lag in the model is the future. The alternative is to specify the spatial weight matrix as a convex combination of several submatrices based on different distance measures (geographical, economic, political, etc.), and to estimate the contribution of each submatrix to the overall matrix. I do not know yet which of these two methods is more promising. Each of these approaches improves the fit of the model, helps to find out which spatial econometric model specifications and which specifications of the spatial weight matrix are outperformed. On top of that, it accounts for the uncertainty the researcher faces in empirical research when computing direct and indirect effects, because the true spatial weight matrix or matrices are unknown.
Spatial Interaction and Spillovers: The Two Laws of Spatial Modelling
HSSL: In your 2024 paper, you formulate two fundamental laws of spatial modelling: units of observation cannot be treated as independent because they interact, and interaction generates spillovers. You also argue that no single approach yet addresses both adequately. What would a framework capable of satisfying both laws need to accomplish that existing models still cannot?
J. Paul Elhorst: I am regularly surprised by the number of studies that still treat spatial units of observations as independent entities. The explanation is that spatial econometrics has become part of mainstream econometrics, causing researchers active in this field to attend far fewer regional conferences and publish far less in regional journals. That is a worrying development, especially because the development of advanced spatial econometric models does not stand still. To cover both laws, the future is a GNS dynamic spatial econometric model with common factors, either in the form of cross-sectional averages or principal components. Although we are getting closer and closer to this model, we are still not there.
Towards a Fourth Generation: Dynamic Spatial Models with Common Factors
HSSL: In your book, you organised the development of spatial econometrics into three generations: cross-sectional models, static spatial panels, and dynamic spatial panels. Do you think we are now entering a fourth generation? If so, what developments-methodological, computational, or data-driven-will define it?
J. Paul Elhorst: I defined the fourth generation model spatial econometric model as the model that also controls for common factors, either in the form of cross-sectional averages or principal components. As said, the future is a GNS dynamic spatial econometric model with common factors.
Methodological advances, however, rarely develop independently of the problems encountered in empirical research. This brings us back to the relationship between applications and the development of spatial econometric methods.
How Empirical Applications Inform Methodological Development
HSSL: Much of your methodological work has developed alongside empirical applications, from regional labour markets and tax competition to FDI, transport and research productivity. Can you recall an application that exposed a limitation in the existing methodology and led you to think differently about the econometric model itself?
J. Paul Elhorst: Through empirical research, you learn much more about the current weaknesses of existing spatial econometric models. Several theoretical-econometric studies turn out to have hardly any added value in applied empirical research. Only the combination makes it possible to bridge the gap between the two.
The Next Challenge: Finding the Right Spatial Weights Matrices
HSSL: Fifty years have passed since Jean Paelinck gave the field its name-an anniversary you marked in the special issue arising from the Groningen conference. Looking forward rather than back, what has spatial econometrics still not solved? And which open problem would you hand to the next generation?
J. Paul Elhorst: Finding the right, read closest to the true, spatial weight matrix for every single spatial lag in the model is the greatest challenge spatial econometric researchers still face. My experience is that authors who criticize spatial econometrics are unparalleled in their ability to explain how not to do it. This is easy. The art is to explain how to do it. This is difficult, and it is my drive.
HSSL: Professor Elhorst, thank you very much for sharing your reflections with the Hellenic Spatial Statistics Lab.